David Pollard: visit to Johns Hopkins

Duncan lectures

1. SOME STATISTICAL ISSUES IN THE CONSTRUCTION OF JURY ARRAYS
   Abstract
   Slides from the lecture.
   Summary of Pollard testimony in State v. Gibbs

2. WHAT IS RANDOMIZATION?
   abstract
   

Short course on asymptotics

• Wed 3/25 : Lecture 1, 3 PM
• Thu 3/26 : Lecture 2, 11 AM
• Fri 3/27 : Lecture 3, 11 AM
• Mon 3/30 : Lecture 4, 3 PM
• Tue 3/31 : Lecture 5, 3 PM
• Wed 4/1 : Lecture 6, 3 PM

• [Thu 4/2 1998 Duncan Lecture (JURY ARRAYS) by David Pollard, 4 PM (in Maryland 110); reception to follow (in Maryland 109)]

• Fri 4/3 : 2nd Duncan talk (RANDOMIZATION) = Lecture 7, 11 AM
• Mon 4/6 : Lecture 8, 3 PM
• Tue 4/7 : Lecture 9, 3 PM
• Wed 4/8 : Lecture 10, 3 PM

Rough outline of material to be covered in talks

• Heuristics. How does one get a limiting distribution for an estimator defined by minimizing a random criterion function? M-estimators. Efficiency: a myth? Why we need uniform approximations. Le Cam's quadratic approximation on a grid--how to get good estimators without pointwise quadratic approximation (and help from a preliminiary root-n consistent estimator).
• Behaviour of estimators under alternatives. Contiguity. Why \exp(N(-\sigma^2/2,\sigma^2)) turns up so often.
• Total variation, Hellinger, and Kullback-Leibler: good ways to measure distances between probability models. Hellinger differentiability. The neat way to get the information inequality.
• LAN (local asymptotic normality). Why it is a clever idea. LAN from Hellinger differentiability.
• The convolution theorem and (maybe) the "local asymptotic minimax theorem". Introduction to the idea of solving a decison-theoretic problem for the limiting Gaussian shift, then deducing a limit theorem in the form of a lower bound.
• Le Cam's distance between experiments. Sufficiency, likelihood ratios. Why the technicalities? (This material will flow into the Duncan Lecture on Randomization.) Bounds via likelihoods, and generalizations.
• More on local asymptotic minimax theorem, using Le Cam's metric.
• Some discussion of recent work of Brown and Low, and Nussbaum. (maybe)
• If time permits I will add some material on minimax rates of convergence. It would fit most naturally after topic 3, but it is more important to start 6 before the Duncan Lecture on Randomization.

  I would also like to work in some discussion of general methods for deriving rates of convergence and limit theory for "abstract minimization estimators": the ultimate comparison theorem.

  There is a whole section of the Asymptopia manuscript on maximal inequalities (empirical process ideas) that I fear I will have to skip over. Maybe that material will have to be discussed over coffee with the true fanatics.